In Greek mythology, what is the name of a male nature spirit with ears and a tail of a horse?

Satyrs are half goat not horse !!

Seems they left an important part out of the picture...

surely that's a centaur in the picture.

David Bulfoni, that's in Roman mythology

The difference is Satyrs had upper body of a man and two horse shape legs with hoofs. Centaur had 4 horse shape legs with hoofs and a man upper body.

That doesn't look like a nymph he's going after in the picture. Were some satyrs bi?

David Bulfoni, In Greek art, it's Horse. In Roman, it's Goat. You are both correct.

David Bulfoni, This seemed strange when I read it. ! ! !